As a general method for producing a weather strip material having a rod-shaped member and a corner member fused to each other, a production method by so-called insert molding is known in which generally an unvulcanized rubber composition of a terpolymer of an ethylene/propylene/non-conjugated diene is profile-extruded and vulcanized to produce a rod-shaped member, the rod-shaped member is charged into one side or both sides of a mold and then an unvulcanized rubber composition of a terpolymer of an ethylene/propylene/non-conjugated diene is injected into the mold cavity, following vulcanization and molding thereof thereby vulcanizing and fusion-bonding a corner part to the rod-shaped member. This method, however, requires the vulcanization step to be conducted twice, is complicated and requires a long operation time, and improvement is thus strongly demanded from the viewpoints of saving in labor, improvement in productivity, reduction in weight, and the like. Accordingly, thermoplastic elastomer compositions, which do not require vulcanization, have been increasingly substituting in recent years for rubber compositions in order to simplify the molding process and reduce the operation time.
However, when thermoplastic elastomer compositions are used in the method described above, the resulting composite molded article is sometimes inferior in fusion strength between a rod-shaped member and a corner member. JP-A 59-221347 describes that an olefin thermoplastic elastomer composition compounded with crystalline poly-1-butene is used as an olefin thermoplastic elastomer composition with an improved fusion-bonding property, but its effect is not sufficient.